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These two relations involving entropy are also useful because they'll let us see how entropy depends on volume and pressure.
这两个涉及熵的关系也非常有用,因为他们告诉我们,熵和体积，压强的关系。
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In other words, if we don't have to worry about entropy or volume equilibrium is achieved when energy is at a minimum.
换句话说，如果我们不担心熵,和体积的平衡,那么能量就得是最小的。
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On the other hand, temperature, volume and pressure are variables that are much easier in the lab to keep constant.
另一方面，温度，体积和压强,在实验室中比较容易保持恒定。
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We could just collect a bunch of data. For a material .What's the volume it occupies at some pressure and temperature?
对一种物质我们可以得到一系列测量数据,在给定的温度和气压下,它的体积是什么？
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And we combine this with first law, which for the case of pressure volume changes we write as this.
结合第一和第二定律,对于压强体积功我们可以这样写。
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OK, now what we'd like to do is be able to calculate any of these quantities in terms of temperature, pressure, volume properties.
现在我们想要做的是能够利用,温度，压强和体积的性质,计算上面的物理量。
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And you already saw last time there was this relationship between the temperature and volume changes along an adiabatic path.
是条绝热路径，而上次你已经看到,沿着绝热路径温度和体积,的变化有这个关系。
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That for an ideal gas it has to be the case that there's no volume dependence of the energy.
我们可以直接推导这个结果,即证明对理想气体，内能和气体体积无关。
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For instance, the pressure and the temperature, or the volume and the pressure.
比如压强和温度，或体积和压强。
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So, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.
我现在所要做的一切就是,考察自由能对,温度，体积和压强的偏导数。
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OK, now, we're going to look at the internal energy, and we're going to pretend that it is explicitly a function of temperature and volume.
好，我们接下来看看内能，我们假设,它是温度和体积的函数。
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So, you do this measurement, you measure with the gas, you measure the pressure and the molar volume.
现在让压强趋于，现在测量气体的压强，和摩尔体积。
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and final points, a relationship between the temperature and volume for the initial and final points.
我们就得到了,初末态的温度,和体积间的关系。
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But it's allowed to say the internal energy is a function of temperature and volume.
但是我们也可以说内能,是温度和体积的函数。
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Now let's change the pressure and temperature and sweep through a whole range of pressures and temperatures and measure the volume in every one of them.
然后改变气压和温度,并且让气压和温度,取便所有可能的数值,测量相应的体积。
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The additional change due to changing pressure volume is certainly measurable.
由于压强和体积的改变带来的,附加变化无疑是可以测量的。
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It has a particular pressure and a particular volume.
它有一个压强和体积。
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If I'm working under conditions of constant temperature and volume, that's very useful.
如果在恒定的温度和体积下,进行一个过程，这是非常方便的。
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It relate state properties to each other.
体积和温度联系起来。
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It relates the pressure, volume, and temperature together.
它把压强，体积，和温度联系在一起。
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You could have the volume and the pressure.
可以是体积和压强。
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We discovered that the quantity dA, under conditions of constant volume and temperature, dA TS And A is u minus TS.
我们发现在恒定的体积和温度下，亥姆赫兹自由能的变化，小于零，is，less，than，zero。,亥姆赫兹自由能A等于内能u减去。
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In general, temperature and volume or pressure.
一般来说写成了温度，体积和压强的函数。
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That is, in real life, the variables that you'd normally control aren't some combination of entropy and these variables, but really their temperature, volume and pressure, any couple of those, might be what you'd really have under experimental control.
在生活中，我们所能控制的,不是熵和其他变量的组合，而是温度，体积，压强，以及其中的两两组合,这些才是试验中所能控制的。
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In this case, V = /P. Have two quantities and the number of moles gives you another property. You don't need to know the volume. All you need to know is the pressure and temperature and the number of moles to get the volume.
以及气体的摩尔数,就可以得到第三个量,知道压强，温度和气体的,摩尔数就可以推导出气体的体积,这称为状态方程,它建立了状态函数之间的联系。
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So now, this equation here relates three state functions together: the pressure the volume, and the temperature. Now, if you remember, we said that if you had a substance, if you knew the number of moles and two properties, you knew everything about the gas.
压强，体积和温度,大家应该还记得,我们提过，只要知道气体的摩尔数,和任意两个状态函数,就可以推导出其他的状态函数，这样，我们可以把它改写成。
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I mean, if the energy is lower to occupy a smaller volume, then if I have this room and a bunch of molecules of oxygen, and nitrogen and what have you in the air, and there are weak attractions between them, why don't they all just sort of glum together and find whatever volume they like.
我的意思是，如果占据小的体积会使能量降低，如果我有这样一个空间,和一些氧气，氮气和其他空气中有的气体，并且分子之间还有微弱的相互作用，为什么他们不黏在一起,然后占据他们所想要占据的体积。
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This is going to end up at a different temperature by the way. You saw this last time in a slightly different way. Last time what you saw is we compared isothermal and adiabatic paths that ended up at the same final pressure, and what you saw is that therefore they ended up in different final volumes.
末态温度是不一样的,上次你们看到的,和这个有一点不一样,上次我们比较的是末态压强,相等的等温过程和绝热过程,因此它们的末态,体积是不一样的。
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But because in many cases we can reasonably either model or measure equations of state, collect data for a material for its temperature, pressure, volume relations, then in fact if we can relate all these quantities to those then in fact we really can calculate essentially all of the thermodynamics. For the material.
但是因为在很多情况下,我们能够合理的给出状态方程的模型,或者通过收集一个物质的，温度，压强和体积之间的关系,来测量其状态方程，所以实际上我们可以给出压强等物理量,和热力学势之间的关系,并计算出所有的热力学势，对于给定的物质。
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